During the CMP process, a wafer is rotated and pressed face down against a rotating polishing pad. Polishing slurry is delivered on the top of pad continuously and forms a thin lubricating film between the wafer and the pad. In this study, a three-dimensional slurry flow model based on a generalized Reynolds equation is developed, which can apply to a rough pad with the compressibility of the pad, and the multi-grid method is used to reduce computational time. According to the force and moment balance equations, the tilted angles and the slurry film thickness can be evaluated. When the pad surface is rough, the squeeze term differentiated by time should be considered in this model due to the rotation of the pad. The influences of applied load, pad speed, wafer speed, pad compressibility, and surface roughness pattern on the tilted angles and the slurry film thickness are investigated. Results show that the variation of the tilted angles becomes more significant for the anisotropic than that for the isotropic during the rotation of the pad. And the slurry film thickness at the center of the wafer increases as applied load decreases or pad speed increases or wafer speed decreases or the compressibility of the pad increases.

The analysis of bearing systems involves the prediction of their static and dynamic characteristics. The capability to compute the dynamic characteristics for hydrodynamic bearings has been added to Bearing Design System (BRGDS), a finite element program developed by Dr. R.W. Stephenson, and the results obtained were validated. In this software, a standard finite element implementation of the Reynolds equation is used to model the land region of the bearing with pressure degrees of freedom. The assumptions of incompressible flow, constant viscosity, and no fluid inertia terms are made. The pressure solution is integrated to give the bearing load, and the stiffness and damping characteristics were calculated by a perturbation method. The static and dynamic characteristics of 60, 120 and 180 partial bearings were verified and compared for a length to diameter (L/D) ratio of 0.5. A comparison has also been obtained for the 120 bearing with L/D ratios of 0.5, 0.75 and 1.0. A 360-journal bearing was verified for an L/D ratio of 0.5 and also compared to an L/D ratio of 1.0. The results are in good agreement with other verified results. The effect of providing lubricant to the recesses has been shown for a 120 hybrid hydrostatic bearing with a single and double recess.

Bearings today need to be able to run at very high speed, providing high positional accuracy for the structure that it supports, and requiring very little or no maintenance. For this to happen, bearings must have tight tolerances and very low or zero friction during operation. This pushes many traditional contact-type bearings to their limits as they often fail due to friction, generating heat and causing wear. By comparison, existing non-contact bearings fare better because of their very low or zero friction. But some have their own problem too. For example, the fact that aerostatic bearings require an air supply means having to use a separate air compressor and connecting hoses. This makes the installation bulky. Aerodynamic and hydrodynamic bearings cannot support loads at zero speed. Both hydrodynamic and hydrostatic bearings may cause contamination to the work-pieces and the work environment because of the use of lubricating fluid. A potential solution to the above-mentioned problems is the new squeeze film air bearing. It works on the rapid squeeze action of an air film to produce separation between two metal surfaces. This has the benefit of being compact with a very simple configuration because it does not require an external pressurized air supply, can support loads at zero speed and is free of contamination. For this research, two squeeze film air journal bearings, made from material of Al 2024 - T3 and Cu - C101 with the same geometry, were designed. The bearing is in the shape of a round tube with three fins on the outer surface and the journal, a round rod. When excited at a certain normal mode, the bearing shell flexes with a desirable modal shape for the squeeze film action. The various modes of vibration of Al bearing were obtained from a finite-element model implemented in ANSYS. Two Modes, the 13th and 23rd, at the respective frequencies of 16.320 kHz and 25.322 kHz, were identified for further investigation by experiments with respect to the squeeze film thickness and its load-carrying capacity. For Cu bearing, the two Modes are also 13th and 23rd at the respective frequencies of 12.184 kHz and 18.459 kHz. In order to produce dynamic deformation of the bearings at their modes, a single layer piezoelectric actuator was used as a driver. The maximum stroke length and the maximum blocking force of the single layer piezoelectric actuator were determined using manual calculation and ANSYS simulation. In the coupled-field analysis, the single layer piezoelectric actuator was mounted on the outside surface of the bearing shell and loaded with an AC and a DC voltage in order to produce the static and dynamic deformation. For the static analysis, the maximum deformation of Al bearing shell is 0.124 μm when the actuators are driven at the DC of 75 V. For the dynamic analysis, the actuators are driven at three levels of AC, namely 55, 65 and 75V with a constant DC offset of 75V and the driving frequency coincided with the modal frequency of the bearing. The maximum dynamic deformation of Al bearing shell is 3.22μm at Mode 13 and 2.08μm at Mode 23 when the actuators were driven at the AC of 75 V and the DC of 75 V. Similarly, the FEA simulation was used for analyzing Cu bearing. Furthermore, the dynamic deformation of both Al and Cu bearing at Mode 13 and 23 are validated by experiments. This research developed two theoretical models that explain the existence of a net pressure in a squeeze film for the levitation. The first model uses the ideal gas law as first approximation whilst the second uses the CFX simulation to provide a more exact explanation. In terms of the load-carrying capacity, Mode 13 was identified to be better than Mode 23 for both bearings. However, at Mode 13, Al bearing has a higher load-carrying capacity than Cu bearing. This is due to Al bearing having a higher modal frequency and amplitude. Finally, the coupled-field analysis for fluid solid interaction (FSI) was studied at both Mode 13 and 23 for Al bearing. The findings are that: a) the fluid force in the squeeze film can affect the dynamic deformation of the bearing shell, especially at high oscillation frequency, more at Mode 13 than at Mode 23 due to the relatively high pressure end-leakage in the latter; b) the dynamic deformation of the bearing shell increases with the gap clearance in a logarithmic manner at Mode 13; and c) the micron levels of gap clearance provide a damping effect on the dynamic deformation of the bearing shell at Mode 13 and at Mode 23, though much less dominant.

Les joints sans contact sont des solutions d’étanchéité optimales pour les systèmes mécaniques fonctionnant à des vitesses relativement élevées. Ils ont une durée de vie importante et ont été proposés pour une utilisation dans les moteurs spatiaux. Une type de joints d'étanchéité sans contact, le joint visqueux, est étudié en détail dans ce travail de thèse au moyen d'une analyse numérique et expérimentale. Ce travail présente un modèle numérique développé pour prédire le comportement du joint visqueux en régime laminaire et turbulent. L’interface liquide-air dans le joint est également étudiée en utilisant une approche CFD basée sur la méthode VOF. La conception et la réalisation d’un dispositif expérimental a permis de confronter les résultats numériques et expérimentaux, l’écart entre les deux approches n’excède pas 10% dans 95% des cas étudiés. / Contactless seals are optimal sealing solution for mechanical systems operating with relatively high speeds. They have an important operation life time, and they were proposed for use in space engines. One sub-category of non-contact seals, the viscoseal, is studied in detail in this work through a numerical and experimental analysis. This work presents a numerical model developed to predict the viscoseal performance in laminar and turbulent regime. Furthermore the sealing performance of the viscoseal is investigated for different geometrical characteristics of the seal. The interface liquid-air in the seal is also studied using a CFD approach based on VOF method. The design and installation of an experimental device allowed the comparison of the numerical and experimental results, the difference between the two does not exceed 10% for 95% of studied cases.

"Two most important events in the history of lubrication theory are attributed to Reynolds and Sommerfeld. Reynolds derived the governing equations for lubricating films in simplifying the Navier-Stokes equations considering thin-film effects. Sommerfeld obtained a closed form analytical solution to the Reynolds equation for the long bearing (one-dimensional case) with fixed constant eccentricity which results in a point symmetric pressure profile compared to an arbitrary (ambient) level. In attempting to reconcile with experimental evidence, Gumbel advanced the argument that sub-ambient pressure in a fluid film is not possible. On the basis that the fluid film would rupture, he put forth that the sub-ambient portion of the Sommerfeld solution should be discarded, a proposition that is commonly recognized as the half-Sommerfeld solution (of Gumbel). Ever since Gumbel suggested this improvement, much interest remains regarding the physical process of rupture in bearing lubricating films. In lubrication literature, cavitation is used interchangeably with rupture to indicate a condition in which an abundance of a gas phase, essentially ambient air, is present in a portion of the bearing clearance. A cogent two-phase morphology for addressing cavitation in long bearings is postulated in order to predict time-dependent fluid behavior from an initial state that is a generalization of Gumbel’s half-Sommerfeld solution. The ultimate steady-state is presumed to satisfy the hypothesis of Swift and Stieber that an ambient condition is reached by the rupture point at an unspecified location simultaneously with a vanishing pressure gradient. A trans-rupture continuity equation, as proposed by Olsson, determines a formula for the speed of a moving rupture point requiring a specific model of the two-phase flow in the rupture region. Employing an adhered film model, sequential application of Olsson’s equation to the rupture points of the intermediate states between the half-Sommerfeld and Swift-Stieber states renders an interpretation of a time-dependent progression towards a steady-state solution. Closed form analytical formulas, which readily combine to provide an exact solution to the Reynolds equation are derived with the start (formation point) of the full-film other than the customary bearing maximum gap and with the rupture point at any assigned intermediate location. Each valid solution for an intermediate state yields an invariant flux that must satisfy a window of constraints to exclude the possibility of sub-ambient pressures. A complete set of such valid solutions exists for each fixed eccentricity and can be depicted as a contour plot of the invariant flux with formation and rupture points as coordinates. The method can readily be extended to two-dimensions, offering a promising alternative to the Elrod cavitation algorithm, which is commonly used in more comprehensive bearing analyses."

An elastohydrodynamic analysis of a rotary lip seal is performed numerically, incorporating both the fluid mechanics of the lubricating film and the elastic deformation of the lip, by solving the Reynolds equation with flow factors. Asperities on the lip surface dominate the behavior of the flow field in the lubricating film and the elastic deformation of the lip. Since previous analyses treated those asperities deterministically, they required very large computation times. The present approach is much less computationally intensive because the asperities are treated statistically. Since cavitation and asperity orientation play important roles, these are taken into account in the computation of the flow factors. An asperity distortion analysis is introduced to obtain a more realistic model of the complex variations in the asperity distribution on the surface of the seal. Results of the analysis show how the operating parameters of the seal and the characteristics of the asperities affect such seal characteristics as the thickness of the lubricating film, reverse pumping rate, power dissipation and load carrying capacity.

We consider mathematical modeling of thin film flow between two rough surfaces which are in relative motion. For example such flows take place in different kinds of bearings and gears when a lubricant is used to reduce friction and wear between the surfaces. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation, which describes the motion of viscous fluids. In thin domains several approximations are possible which lead to the so called Reynolds equation. This equation is crucial to describe the pressure in the lubricant film. When the pressure is found it is possible to predict vorous important physical quantities such as friction (stresses on the bounding surfaces), load carrying capacity and velocity field. In hydrodynamic lubrication the effect of surface roughness is not negligible, because in practical situations the amplitude of the surface roughness are of the same order as the film thickness. Moreover, a perfectly smooth surface does not exist in reality due to imperfections in the manufacturing process. Therefore, any realistic lubrication model should account for the effects of surface roughness. This implies that the mathematical modeling leads to partial differential equations with coefficients that will oscillate rapidly in space and time. A direct numerical computation is therefore very difficult, since an extremely dense mesh is needed to resolve the oscillations due to the surface roughness. A natural approach is to do some type of averaging. In this PhD thesis we use and develop modern homogenization theory to be able to handle the questions above. Especially, we use, develop and apply the method based on the multiple scale expansions and two-scale convergence. The thesis is based on five papers (A-E), with an appendix to paper A, and an extensive introduction, which puts these publications in a larger context. In Paper A the connection between the Stokes equation and the Reynolds equation is investigated. More precisely, the asymptotic behavior as both the film thickness <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" /> and wavelength <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmu" /> of the roughness tend to zero is analyzed and described. Three different limit equations are derived. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high frequency roughness regime). In paper C we extend the work done in Paper A where we compare the roughness regimes by numeric computations for the stationary case. In paper B we present a mathematical model that takes into account cavitation, surfaces roughness and compressibility of the fluid. We compute the homogenized coefficients in the case of unidirectional roughness.In the paper D we derive a mathematical model of thin film flow between two close rough surfaces, which takes into account cavitation, surface roughness and pressure dependent density. Moreover, we use two-scale convergence to homogenize the model. Finally, in paper E we prove the existence of solutions to a frequently used mathematical model of thin film flow, which takes cavitation into account.

The ageing population has become more active and live longer, these patients require hip replacement surgery at a younger age. Artificial hip implants, consisting of the acetabular cup and femoral head, affect the lives of many people, and the longevity of these implants pose significant concerns (rarely longer than 17 years). To help understand the lubricating performance of such a system, a hip joint model was built based on the Reynolds equation; the model developed simulated hydrodynamic lubrication. A steady-state angular rotation model was built whereby it was concluded that such motion would not support any load due to the anti-symmetric nature of the resultant pressure distribution (anti-symmetric about the axis of rotation). The pressure distribution from the steady-state rotation simulation contained a pressure source and sink which converged to the centre of the cup and whose pressure value increased in magnitude, as the eccentricity ratio increased. Infeasible results were obtained when the intermediary pressure constraint, allowing only positive pressure values, was implemented. The results obtained were not representative of the problem and it is recommended that this constraint not be implemented. The transient walking cycle model showed that a fluid with viscosity of 0.0015Pa.s is not sufficient to support a load in the walking cycle under conditions representative of hydrodynamic lubrication. Increasing the fluid viscosity promoted better results in the hydrodynamic model. Increasing the femoral head radius and decreasing the radial clearance between the components also improves the possibility of hydrodynamic lubrication. It is recommended that the model should be extended to investigate elasto-hydrodynamic lubrication. If possible, the effects of a boundary lubrication model should be investigated, as it is believed to be a major contribution to the lubrication of hip joints. / Dissertation (MEng)--University of Pretoria, 2008. / Chemical Engineering / unrestricted

The objective of this Master’s thesis is to find shape optimal design based on min- imizing friction force of thrust bearing by using genetic algorithm(GA) which is one of an optimization toolbox in Matlab. Reducing the friction force of thrust bearing is one way of making shaft to decreasing friction losses. With four parameters of thrust bearing geometry number of segments(m), angle of running surface(), segment inner radius(R0), and segment outer radius(R1) substitute in Reynolds’ equation. In order to know friction force, it is necessary to generate a connecting variable, oil film thickness(h0) from loading capacity(W ) and revolution per minute(rpm). Friction power loss, as well as weight func- tion conclude the final shape optimization of thrust bearing: m = 7, = 0.1, R0 = 15 mm, and R1 = 20 mm.

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